After the death of Arch-Mage Savos Aren, Mirabelle Ervine gives the Dragonborn the item. Shortly before his death, Aren gave the Torc to Mirabelle, saying that she would know what to do with the item when the time came. When the Dragonborn tells her that the Staff of Magnus is in Labyrinthian, she realizes that Aren intended for her to give the Torc to the Dragonborn. She does so, saying that the Staff is critical to stopping Ancano, who has sealed himself in the Hall of Elements at the College of Winterhold with the Eye of Magnus.
The Dragonborn must then travel to Labyrinthian, and use the Torc on the Ceremonial Door in order to unlock it and proceed with the quest.
The Torc can be pickpocketed from Mirabelle; however, if it is, it will not unlock the Ceremonial Door and the quest will become impossible to complete.